Question

Express the complex number in trigonometric form.

2 - 2i

Answer 1

@robtobey please help

Answer 2

I know we have the formula a+bi=r(cos theta) + i(sin theta)

Answer 3

r=square root of a^2 + b^2

Answer 4

r=square root of 8 and tan=-1

Answer 5

you need two numbers, \(r\) and \(\theta\)

Answer 6

yeah \(r\) you get via pythagoras

in your example it is \(2\\sqrt2\)

Answer 7

ooops
\[r=2\sqrt2\]

Answer 8

How do I find out \[\theta \]?

Answer 9

should be clear from the picture

Answer 10

you can use either \[-\frac{\pi}{4}\] or
\[\frac{7\pi}{4}\]

Answer 11

how did you get pi/4 and 7pi/4?

Answer 12

-pi/4

Answer 13

by looking

Answer 14

over 2, down 2
should be clear yes?

Answer 15

How can your go over 2, down 2 on a unit circle?

Answer 16

you don't but the point is not on the unit circle since the modulus is \(2\sqrt2\)

Answer 17

forget the unit circle for a second
'if you go over 2, down 2, what is the angle ?

Answer 18

45

Answer 19

oh okay, i get it now

Answer 20

it is not 45 degrees because you are not in the first quadrant

Answer 21

315 then

Answer 22

or -45 degrees

Answer 23

so that would make it \[2\sqrt{2}(\cos 7\pi/4) + i \sin 7\pi/4\]

Answer 24

Thanks

Answer 25

yes
yw